Roboguru

Diketahui . Jika  dan . Tentukan proyeksi skalar orthogonal .

Pertanyaan

Diketahui straight a with rightwards arrow on top equals 3 straight i plus 2 straight j minus straight k comma space straight b with rightwards arrow on top equals 2 straight i plus 3 straight j space dan space straight c with rightwards arrow on top equals straight i plus straight j minus straight k. Jika straight u with rightwards arrow on top equals straight a with rightwards arrow on top plus straight b with rightwards arrow on top dan straight v with rightwards arrow on top equals straight b with rightwards arrow on top plus straight c with rightwards arrow on top. Tentukan proyeksi skalar orthogonal straight u with rightwards arrow on top space pada space straight v with rightwards arrow on top.

Pembahasan Soal:

Diketahui straight a with rightwards arrow on top equals 3 straight i plus 2 straight j minus straight k comma space straight b with rightwards arrow on top equals 2 straight i plus 3 straight j space dan space straight c with rightwards arrow on top equals straight i plus straight j minus straight k.
straight u with rightwards arrow on top equals straight a with rightwards arrow on top plus straight b with rightwards arrow on top dan straight v with rightwards arrow on top equals straight b with rightwards arrow on top plus straight c with rightwards arrow on top.

Maka, 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight u with rightwards arrow on top end cell equals cell straight a with rightwards arrow on top plus straight b with rightwards arrow on top end cell row blank equals cell open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses plus open parentheses table row 2 row 3 row 0 end table close parentheses end cell row blank equals cell open parentheses table row 5 row 3 row cell negative 1 end cell end table close parentheses end cell end table

dan

table attributes columnalign right center left columnspacing 0px end attributes row cell straight v with rightwards arrow on top end cell equals cell straight b with rightwards arrow on top plus straight c with rightwards arrow on top end cell row blank equals cell open parentheses table row 2 row 3 row 0 end table close parentheses plus open parentheses table row 1 row cell negative 1 end cell row 1 end table close parentheses end cell row blank equals cell open parentheses table row 2 row 2 row 1 end table close parentheses end cell end table

Mentukan proyeksi skalar orthogonal straight u with rightwards arrow on top space pada space straight v with rightwards arrow on top.

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar stack straight u subscript straight v with rightwards arrow on top close vertical bar end cell equals cell open vertical bar fraction numerator straight u with rightwards arrow on top cross times straight v with rightwards arrow on top over denominator open vertical bar straight v close vertical bar end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator 5 cross times 2 plus 5 cross times 2 plus open parentheses negative 1 close parentheses cross times 1 over denominator square root of 2 squared plus 2 squared plus 1 to the power of 1 end root end fraction close vertical bar end cell row blank equals cell open vertical bar fraction numerator 10 plus 10 minus 1 over denominator square root of 9 end fraction close vertical bar end cell row blank equals cell 19 over 3 end cell end table

Jadi, proyeksi skalar orthogonal straight u with rightwards arrow on top space pada space straight v with rightwards arrow on top adalah19 over 3.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Mei 2021

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